In some of the conventional internal combustion engines equipped with a fuel injection mechanism, the fuel supply to all of the cylinders of the engine is cut off upon deceleration until the rotational speed of the crankshaft of the engine falls below a predetermined value such as 1,300 r.p.m. inasmuch as engine output is not required when the throttle valve of the engine is fully closed. This cut-off of fuel supply results in effective engine braking and improvement of its fuel consumption characteristic. In such an engine, the fuel supply is reestablished when the rotational speed of the engine crankshaft falls below the predetermined value in order to prevent engine stall. According to the above mentioned apparatus, since all of the cylinders are enabled (fueled) or disabled (non-fueled) at once depending on whether the rotational speed is above or below the predetermined value, the engine produces an impact or shock which will have an effect on the vehicle body. It will be understood that such an impact or shock is uncomfortable for the vehicle occupants.
Furthermore, the predetermined value at which the reactivation of the engine cylinders takes place has to be set at a relatively high value in order to prevent engine stall. However, this predetermined value is preferably as low as possible to improve fuel economy.